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It will have to be fixed before you drive it very far. If the battery light is on the alternator is not charging, your not going to make it very far before the battery goes dead. Your local parts store will be able to test the alternator on the car, most if not all will do it for free. Based on the battery light I am confident it's the alternator, but ...

26 - Battery Group size (determines the dimensions of the battery: http://www.rtpnet.org/teaa/bcigroup.html)
R - You are correct, this means the terminals are reversed.
5N - Not sure what this part means!

It sounds like you've got a leaking headgasket - the oil is leaking into the engine, which is why the machinic couldn't find the source (though I'd except any decent mechanic to spot HG failure symptoms). Does it also tend to smoke a lot? Particularly blue-ish smoke.
You've spotted oil in the coolant, have a look for coolant in the oil (a thick ...

The oil in your coolant is significant. There are several places oil can enter the coolant, head gasket as mentioned, but also a cracked head or block, a failing oil cooler, as well as accidental filling. If you have had cooling system work done and an oil contaminated water can was used to fill the cooling system for instance this would have introduced the ...

I had a similar problem some years ago and it turned out to be a blocked breather on the fuel tank.
Next time it happens to you, provided you are somewhere that it's safe to do this, jump out of the car and pull the fuel filler cap off and listen around the neck of the fuel tank of a whooshing noise, as though air is being sucked into the tank.
If this is ...

If you are looking for a true dollar cost per km, then do a stock rebuild on the engine. The small amount of abuse from the hp gain you are talking about can be easily absorbed by internals of a stock engine. You just need to ensure you are doing things right. There are several things you can do while rebuilding an engine which will help with longevity:
...

Take the starter off, take it down to your nearest AutoZone/O'Reilly's/Checker/etc. auto parts store and have them bench check it for you. I'll bet your solenoid is no longer functioning, and therefor your starter has quit working.

If you say all the hoses and clamps are in good order, then the only other things that come to mind are the wastegate and exhaust manifold. Either the wastegate is opening too soon, or the exhaust manifold is leaking from the gasket or a crack. This would mean that either you lose boost too early, or you never get enough boost in the first place.
Or, if ...

STOP DRIVING IT until you get the exhaust leak fixed .You can easily be overcome by the carbon monoxide.While driving the air moving under the car is sweeping away the exhaust,when you are still the exhaust is leaking into the passanger compartment.

I wish you luck. In my experience any car that's 10 years old or more is probably leaking somewhere, just most times people haven't noticed yet (although, they eventually notice when the floor rusts through and falls out). The causes of leaks are multitude. You just have to go around every spot where there's a break in the metal (antennas, windows, trim, ...